How to improve the accuracy of the discrete gradient method in the one-dimensional case

Abstract

We present a new numerical scheme for one dimensional dynamical systems. This is a modification of the discrete gradient method and keeps its advantages, including the stability and the conservation of the energy integral. However, its accuracy is higher by several orders of magnitude.

7 pages plus 7 figures

References in corpus (2)

• An orbit-preserving discretization of the classical Kepler problem
• Long-time behaviour of discretizations of the simple pendulum equation

Cited by in corpus (11)

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• Comment on `conservative discretizations of the Kepler motion'
• On the exact discretization of the classical harmonic oscillator equation
• Some implications of a new definition of the exponential function on time scales
• Locally exact modifications of numerical integrators
• Locally exact modifications of discrete gradient schemes
• Improving the accuracy of the AVF method